Homework Sourseassume that x has a normal distribution with the specified m
assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability.
?=4.2 ?=1.7 round to 4 decimals
P(3<x<6)
?41; ?=15
P(50<x<70)
?13.8 ?=3.7
P(8<x<12)
?=102 ?=10
P(x>120)
assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability.
?=4.2 ?=1.7 round to 4 decimals
P(3<x<6)
?41; ?=15
P(50<x<70)
?13.8 ?=3.7
P(8<x<12)
?=102 ?=10
P(x>120)
?=4.2 ?=1.7 round to 4 decimals
P(3<x<6)
?41; ?=15
P(50<x<70)
?13.8 ?=3.7
P(8<x<12)
?=102 ?=10
P(x>120)
Solution
for normal distribution
P(X <x) = P(Z < x- u/std)
a)
P(3<X<6) = P(X<6) - P(X<3)
= P(Z<6-4.2/1.7) - P(Z < 3-4.2/1.7)
= P(Z < 1.0588) - P(Z <-0.70588)
= 0.8552 - 0.2401
= 0.6451
b)
P(50 <X <70) = P(Z < 70-41/15) - P(Z < 50-41/15)
= P(Z < 1.9333) - P(Z < 0.6)
= 0.9734 - 0.7257
= 0.2477
c)
P(8<x < 12) = P(Z < 12-13.8/3.7) - P(Z < 8-13.8/3.7)
= P(Z < -0.4865) - P(Z <-1.5676)
= 0.3133 - 0.0585
= 0.2548
d)
P(X > 120) = P(Z > 120 - 102/10)
= P(Z > 1.8)
= 0.0359
